Heat Definition and 1000 Threads

I want to solve the heat equation below: I don't understand where the expression for ##2/R\cdot\int_0^R q\cdot sin(k_nr)\cdot r \, dr## came from. The r dependent function is calculated as ##sin(k_nr)/r## not ##sin(k_nr)\cdot r##. I don't even know if ##sin(k_nr)/r## are orthogonal for...

In AB, dU=0 (Isothermal) Hence dQ=dW W1= RT ln(2V/V) = RT ln(2) = 800R*ln(2) Q1=W1 = 800R*ln(2) Q2= Cp(300-800)=-500Cp = -500*2.5R Q3 = Cv(800-300) = 500Cv = 500*1.5R So Q= 800R*ln(2) -500*2.5R + 500*1.5R = 800R*ln(2) -500R Hence net heat absorbed is 800R*ln(2) -500R But. Suppose I find...

Summary:: I need to know the preheat temperature of the water entering the gas boiler (which i think is the outlet temperature of the cold water Tc,o leaving the heat exchanger) Hi, I'm doing a design project of a hairpin heat exchanger. The problem is: In a public shower, the city water is...

PROBLEM: A 120 gallon tank (26" diameter, 60" height) containing 40 Gallons of water is heated up until the tank ruptures from overpressure at 125 PSI (maximum tank rating). How to calculate the initial escaped steam velocity at the ruptured tank, assuming the gash is 2 feet long in the...

I post the working in the attached file

I've tried to show b) by using the sine Fourier series on ##[0,2a]##, to get ##g_k = \Sigma_{n=0}^{2a} \sqrt\frac{2}{a} Sin(q_k x)## Therefore ##\sqrt\frac{2}{a} = \frac{1}{a} \int_0^{2a} Sin(q_kx)g_k dx## These are equal therefore it is an orthonomal basis. I'm not sure if this is correct so...

Hi Folks, I'm 70, so I often confuse myself! Ha ! My question is: Do materials both absorb and release heat equally? So when I evaluate different materials for thermo efficiency, does a copper pipe's surface absorb solar heat at the same rate it gives off heat? My question is specific to a...

Hi, I'm looking to find a very very basic model to calculate the heat transfer coefficient in a tube with given heat power exchanged ##Q##. The fluid inside the tube starts sub-cooled (##T_{in}## is known) but exits the tube with a quality of steam around 0.15 (pressure is supposed constant)...

Please help answering

I am considering building this type of heat exchanger, as I have seen several youtube videos on the build. The inside tube is aluminum, I am planning on building one from the top of my roof to nearly the floor, so ill say 5 feet. I am thinking of using a 1.5" inch aluminum tube, and bringing in...

When the delta t and x approached zero, assumably it results in the whole fraction to be zero. The slide shows it will be ##k^2##. Can someone explain this to me, please? P.S. I have tried to search this up, I could not find anything related to the confusion.

So really i am just unsure how to answer the last part of the question. I am unsure how to apply the low and high temperature limits the way i have done it. Do i set upper/lower limits on the integral and solve? If so i am not sure what to put Here is what he book has for 3d

I have used the heat equation and am not able to get the initial heat. This is what I have so far: 81060 = 7 * 140 * (change in temp) - (7 * 11300) + 7 * 140 ( change in temp) I found the change in temp to be 81.71K. But that does not help me with the initial temperature!

I'm working on a project to replace a couple of vacuum pump skids for a lab campus. The existing pumps are water-cooled, liquid-ring pumps. Since they are water cooled, there is effectively no heat rejection into the mechanical room(s) except through un-insulated exhaust pipes. The new pumps...

Summary:: Determine the temperature distribution in a bar (very long– 2D) with rectangular cross section, in steady state, with imposed flux at one face, convection at the opposing face (Tinf, h), and imposed temperature (T1) at the two remaining walls. I am trying to find the analytical...

Hi. I'm a science fiction author whose first novel Hemispheres, published through RockHill Publishing, explored a tidal-locked planet (Gliese 581g) where a group of activists increased its rotation to bring daylight cycles to both hemispheres. Now I'm writing the sequel, and there's ecological...

My goal is to determine the ideal amount of air flow, in order to keep CO2 below 1000ppm and to minimize heat loss. I calculated the following based off a similar post in this forum, and I am hoping this can be verified so I know that i am in the right ballpark and going in the right direction...

Are there any known instances of heat transfer via conduction or convection happening at relativistic speeds? Is this even possible or is there a non-relativistic limit to how fast heat can transfer in these ways, like how sound can only move so fast?

I have completed Q1 and Q2 (i - iii); not sure if I correct in my answers; i would be very grateful for any feed back, thanks.

In our class, we're using Wassermann's Thermal physics as textbook. I always try to solve all question which included in Text book. But sometime when I meet a problem that look like easy but actually hard, I'm so embarrassed. This problem do also. First, in the textbook grand potential for van...

Hi everyone This is a quick Q but I don't understand why I got it wrong This is what I have done Could anyone let me know where I went wrong? Thanks for any help!

I have to design and assemble a solar water heater for a small Anaerobic Digester system. It will have two connected sections, using pipe, ... one assembly section to collect solar heat, one assembly to radiate the heat. Attached is an illustration. Please disregard the pipe arrangement design...

I have a question about building efficient heat engines in outer space. In theory you could have a hot reservoir heated by the sun that was several hundred degrees C, and a cold reservoir that was very cold - maybe 50K - 100K or even colder. Thus, theoretically at least, a heat engine could be...

There used to be sold a style bicycle handlebar bags that used what I think is a formed spring steel rod that fit over the handlebars and looped under the handlebar stem that supported a handlebar bag. For whatever reason this style does not appear to be available any more. I think it is a...

Hello everybody! I was wondering today if physically, it'd be possible for the world to develop an air conditioner without an outdoor heat unit? I know this seems to violate the second law of thermodynamics, but the known version of the second law thermodynamics only consider this is impossible...

Hi, I am trying to calculate the heat flow across the boundary of a solid cylinder. The cylinder is described by x^2 + y^2 ≤ 1, 1 ≤ z ≤ 4. The temperature at point (x,y,z) in a region containing the cylinder is T(x,y,z) = (x^2 + y^2)z. The thermal conductivity of the cylinder is 55. The...

The specific heat capacity at constant volume and the specific heat capacity at constant pressure are intensive properties defined for pure, simple compressible substances as partial derivatives of the functions u(T, v) and h(T, p), respectively, $$c_v=\left ( \frac{\partial u}{\partial T}...

Hi, I was recently attempting the following problem from heat transfer and I didn't really know how to include the fin amongst the other thermal resistances in the problem. The key quantities are: ## T_{in} = 20 C ##, ## T_{out} = -5 C ##, ## h_{inner} = 5 W m^{-2} K^{-1} ##, ## h_{outer} =...

I am looking for a passive way to convert a supply of hot air into warm pool water. My pool can be in the low 70s without heat. Looking to get a 10 degree lift in pool temp. Pool is in-ground and relatively small at 8,500 gal. Water flow rate through the radiators can be regulated by valves...

You can use the change in volume to find how much ice turned into water, and then find the energy required to melt that ice - that I have no problems with. But then work done by piston = change in internal energy of ice/water combination (which we found) + heat released to the bath. And we...

When we measure 'the rate of conduction heat transfer'=Q , we assume that the hot side and the cold side's area are same. But if the both side's area is different to each other, how can i know the rate of conduction heat transfer? like below figure. Would you like to help me?? Thanks.

According to me a=b cause what I have been learning is R is gas constant and hence it will be same for both. But the solution have says something else. According to them Cp-Cv=R/M where M is the molecular mass of gas. So is the above mentioned formula correct? Do we have to take that M term...

I couldn't solve this problem. Any tips or help would be appreciated. If I am violating against any rules please comment, as this is my second post :-).

Hi all, If in a room, a lighting design was carried out and the room will contain 4 no, LED luminaries with a total wattage of 80. My query relates to what would a reasonable figure or percentage be to use as heat gain from the light. Of the 80 watts, how much of it would go into heat? I am...

In a parallel connection heat is produced. R1 = 5 Ohm R2 = 10 Ohm What is the relation of W1/W2? 1:4 1:2 2:1 1:8 3:1 I’d tend to say 1:2, but I am not really sure…

I thought I'd calculate how much heat was required to melt the Iron Throne, and then multiply that by the number of flame-gushes during the sack of Kings Landing, to get a total amount of energy expended. Then I'd convert that to calories and use the average number of calories per goat to...

Please see if you agree with how I am calculating the number of bricks required to reduce cooling off of my house overnight in the winter when I'm not there (sleeping) to feed logs into the stove. The estimated weight of each log that I would normally be burning in my stove is 8.6 pounds...

I've conducted this experiment yesterday. The main goal of this experiment is to find a gas constant R and compare it with its theoretical counterpart but I get stuck in calculating a Cv so I tried to find out what's wrong with my calculations by trying to calculate a Cv from the given data...

I came upon a realization recently. The early universe is always described to have begun in a state of extremely low entropy and it's been increasing ever since. But the same amount of stuff exists now as it did back then. Only thing that's changed is how big the universe is now vs then. So...

Nota that the path a to b is isothermal since J is proportional to L, then we can find the value of T_a and T_b using the equation of state and the figure. We have, \begin{equation} J_0=\alpha L_0T_b \end{equation} or \begin{equation} T_b=T_a=\frac{J_0}{\alpha L_0}=T_0 \end{equation} Also, by...

If a heat engine converts heat into "work", will ice used to run a Stirling heat engine last longer than ice allowed to melt by itself? To try and answer this, I obtained a Stirling engine and ran this experiment: With the engine running: And not running: Without the engine running the...

The second question is where I'm lost. The answer to the first question is 5.39 grams. The second is 10.3 grams. Until I saw the answer I was setting the equation up as if some of the original steam had condensed. But it appears that some of the original water changed into steam. Is it necessary...

Something I've been thinking about recently is like how much heat would it take to evaporate an entire lake in less than a second. Or something like Tungsten Steel. The main question is does an increase in heat increase the rate of its change in structure? Sorry for the boring question.

In my city (USA) typical older houses have "100 Amp service" so their peak electric usage is limited to 100 Amps. In considering what sort of electric air conditioning system to install in such a house, peak usage is major consideration. Generally speaking, which type of residential unit...

I would like to fully understand two parameters involved in convection heat transfer systems. I have read the document https://fenicsproject.org/pub/tutorial/sphinx1/._ftut1005.html, and I am interested in the parameters ##r## and ##s## in eq. 69. As far as I understand, when one solves the...

Hi, what I've done so far is solving equation 2) for ##U##, and replacing what I get in equation 1). Then, ##c_V## is equal to the partial derivative of ##S## with respect to T times T, so I've done that. The derivative is ##CNR/T##, so ##c_V=CNR## but those aren't the correct units for ##c_V##.

I have come across this problem from this booklet: https://www.ioc.ee/~kalda/ipho/Thermodyn.pdf

Hello all! I would like to know what chemical/physical properties influencies the specific heat. For example, why are specific heat of metals smaller than the specific heat of water, and why do ice and steam have a smaller specific heat than liquid water do.

Q1=2.5(390)(90-30) =58500 Q2=2.5(4000) = 10000 Qtotal = 58500+10000 Q=68500 =6.8x10^4 my teacher sent this as a homework but the options were 4.9x10^4 J 1x10^4 J 6.8x10^5 J 5.9x10^4 J im confused is is this a typo or did i do something wrong